d/dt

Derivative

Continuous

The Derivative block computes the numerical time derivative (rate of change) of an input signal using backward difference approximation. An optional low-pass filter parameter can be used to reduce noise amplification.

Mathematical Model

Pure derivative (filterCoefficient = 0, default)

\frac{dy}{dt} \approx \frac{u_n - u_{n-1}}{\Delta t}

Filtered derivative (filterCoefficient = N > 0)

Transfer function: H(s) = N*s / (s + N)
Discrete: D[k] = (N * (u[k] - u[k-1]) + D[k-1]) / (1 + N * Δt)

where:

u_n is the current input
u\_{n-1} is the previous input
Δt is the sample time
N is the filter coefficient (higher = less filtering)

Inputs & Outputs

Direction	ID	Label	Type	Status
→ In	`in`	Input	number	Required
← Out	`out`	Output	number	Output

Parameters

Parameters	Label	Type	Default	Description
`filterCoefficient`	Filter Coefficient (N)	number	`100`	Implements H(s) = N·s/(s+N). N=0 disables the block (output = 0). N sets the filter bandwidth in rad/s — higher N gives a faster, more accurate derivative but amplifies noise. Practical range: 5–100. Rule of thumb: N ≈ 5–10× the highest signal frequency of interest.

Usage Examples

Ramp Derivative (1 second simulation)

Linear ramp with slope 2 V/s goes into Derivative block. The output is a constant 2 V, showing that the derivative of a linear signal is its slope.

PID Controller D-Term

Connect the error signal to Derivative, scale with Gain, sum with P and I terms.

Remarks & Best Practices

Pure Differentiation: Backward difference formula, optionally filtered
Numerically Noisy: High-frequency content is amplified without filtering; use filterCoefficient to mitigate
Essential for Control: Forms the D-term in proportional-integral-derivative controllers
Inverse of Integrator: Complementary to the Integrator block for system analysis
First Step: Always outputs 0 on the first step to avoid initialization spikes

Related Components

Integrator: Inverse operation (time integration)
Gain: Signal scaling for proportional gain
TransferFunction: General continuous-time dynamics
PIDController: Has built-in filtered derivative